1. Introduction
It has been more than four years since an earthquake and
tsunami caused an accident at the Fukushima Daiichi nuclear power
plant in Japan resulting in repeated ﬁres and three reported core
meltdowns. At the latest count, the accident had caused $166 billion in damages1 [1] and at least 573 immediate deaths from the
evacuation, along with hundreds of future deaths related to cancer anticipated to occur [2]. Somewhat sweeping industry reforms
were called for, and public acceptance of the technology plummeted [3]. Supporters of nuclear power were quick to point out
that a complete phase out would complicate efforts at mitigating
greenhouse gas emissions from the electricity sector [4] and could
lead to cumulative global losses in global gross domestic product
[5].
The March 2011 Fukushima nuclear accident is a poignant
reminder that disasters of enormous consequences can occur in
the nuclear industry. But how often and with what severity? These
two questions constitute the core of sound risk management, which
requires identifying and quantifying such potential losses and their
frequencies. For most natural and human-made catastrophes such
as earthquakes, meteorites, avalanches, mountain collapses, forest

夽 One of the authors of this paper is an editor for Energy Research & Social Science.
They were not involved in managing the peer review process for this article.
∗ Corresponding author. Fax +45 3032 4303.
E-mail address: sovacool@vt.edu (B.K. Sovacool).
1
Updated to US$2013 and adjusted to monetize human fatalities. Originally
reported as $150 billion in $2010 damages.

ﬁres, hurricanes, epidemics, health care costs, war sizes, terrorist
intensities, cyber risks, dam failures, industrial disasters, and so
on, plentiful historical data has allowed scientists and engineers to
determine the distributions of losses.
The admittedly favorable situation of a paucity of nuclear accidents, combined with scantly available public historical data, has
prevented any such statistical analysis. Nuclear engineers have thus
resorted to the classiﬁcation of hypothetical accident scenarios
deemed credible and of their potential consequences. The common industry approach to assessing nuclear accident risk depends
on a technique known as probabilistic safety analysis (PSA), which
assigns probabilities and damage values to particular failure scenarios. Nonetheless, such techniques are known to poorly predict
events and to under-appreciate incidents that cascade into failures
[6–11,12].
Similarly, the IAEA (International Atomic Energy Agency) provides the INES (International Nuclear Event Scale) to communicate
the severity of nuclear accidents on a progressive discrete scale
of 1 (anomaly) to 7 (major accident), meant to correspond to
the amount of radiation released by order of magnitude. Yet its
approach has been critiqued for offering relatively crude scores, for
reporting only a fraction of known events, for not being transparent in its methodology, and for being more of a public relations tool
(propaganda) than a meaningful metric [9,13]. For instance, there
are about 12,000 events reported by French operators every year,
of which 600–800 are classiﬁed annually as “signiﬁcant for nuclear
safety,” yet little to none of these show up on the INES database, and
such unreported events occur at just 15% of the currently operating
world nuclear ﬂeet [14].

In this study, we summarize the results of a statistical analysis of a dataset of 216 events (incidents and accidents) occurring
in nuclear energy systems [15], a dataset that is twice as large as
any of the previous best ones available in the scientiﬁc literature
[8,16], but we refrain from using the INES data directly. Instead,
we use the estimated cost in USD (US dollars) as the common metric that allows one to compare often very different types of events
across the nuclear fuel cycle. This dataset has more than three times
the number of accidents compared with studies using solely the
INES data, providing a much better basis for statistical analysis
and inference, and a better comparative tool for reassessing the
safety of nuclear power. Following Chernobyl, several authors proposed utilizing a monetary value of damage severity to make events
comparable, and use a rate measure normalized by the number
of reactor operating years to consider frequency [17–19]. This is
what we have done here, but extending the range of analysis well
beyond 1986 to include Fukushima and other nuclear events leading up until the end of 2014. The dataset has been published online2 ,
where the public is encouraged to review and recommend additions and modiﬁcations with the intention of continually expanding
and improving the quality of the data.
2. Methods
There are many ways to quantify the risk of accidents in nuclear
energy systems. The Farmer curve is one of the standard tools
of nuclear risk assessment, with the risk deﬁned as “probability × consequences” [20]. Typical Farmer plots display the annual
frequency of fatalities or of property damage from human made
sources of risk. Remarkably, the nuclear risks reported in Farmer
plots are fundamentally different from all previously mentioned
risks, in that the distributions for nuclear event losses are always
thin-tailed and Gaussian-like, presenting a downward concave
shape in the standard log–log representation.
The appearance of the Soviet Union’s Chernobyl accident in
1986 and of Japan’s Fukushima Daiichi nuclear power plant accident, after the tsunami on 11 March, 2011, seem at odds with
the statistics implied by the Farmer curves. Actually, following the
Chernobyl accident, Hsu [17] and Sengor [18,19] suggested a different approach, based on the reasoning that the number of fatalities
is an incomplete, if not misleading, metric for measuring nuclear
losses given the difﬁculties in assessing long term real mortality
in addition to early morbidity and mortality. Indeed, this metric misses many other dimensions and also prevents quantitative
comparisons. Hsu in particular made the point that the statistical
analysis of earthquake risks, for instance, would have missed the
fundamental Gutenberg–Richter magnitude–frequency law [21] if
seismologists had focused on only the few large earthquakes. By
considering a range of event sizes above which the data is known
to be sufﬁciently complete, or at least representative, one can identify possible statistical regularities that are relevant to the largest
events.
Here, we analyze the distribution of losses resulting from all
possible types of nuclear events from 1952 to 2014. To be consistent with both the INES, as well as earlier peer-reviewed studies
[8,9], we assessed events across the entire nuclear fuel cycle—that
is, not only at nuclear reactors and power plants but also at uranium mills, fuel enrichment facilities, reprocessing stations, and
nuclear waste repositories. In addition to maintaining consistency,
this inclusion of non-reactor events is also necessary to trace the full
impact of nuclear power technology on society as well as to account
for the fact that many sites prone to accidents concentrate multi-

2

See https://tasmania.ethz.ch/index.php/Nuclear events database.

97

ple elements of the fuel cycle in one location.3 Searching historical
archives, public utility commission ﬁlings, regulatory reports, and
other sources explained in SM1, we created a unique dataset of 216
nuclear events, with 104 of these events having at least $20 million in inﬂation-adjusted cost.4 In addition, whenever events had
the same dependent cause, such as Fukushima, we treated them as
a single occurrence. As it is important to evaluate the number of
accidents relative to the number of reactors in operation, we have
normalized our assessment to operational reactor data from the
IAEA [22].
To be fair, a few caveats and limitations deserve mentioning. In
this study, we focus only on damage and loss of life from nuclear
accidents, and not other externalities such as lung cancer risks from
coal mining or particulate pollution from petroleum-fuelled automobiles. Consequently, our study details the risks present from
continuing to operate existing reactors, it does not assess the risks
from not operating them (such as greater reliance on fossil fuels)
[4]. Also, as is typically the case in data such as this, there is an event
severity level below which events are less frequently reported, or
even noticed—making our analysis conservative because of incomplete data. We base our analysis on the current reactor ﬂeet, heavily
tilted towards older light water reactors (often called “Generation
II” technology), not state-of-the-art designs such as the European
Pressurized Reactor or “paper” units at the conceptual stage such
as small modular reactors, primarily because there is insufﬁcient
operating experience for their statistical analysis, but also since the
adoption of these designs is uncertain. Our characterization of the
current risk level, and its use for forecasting, presumes that 388
reactors remain in operation, and does not include any potential
improvements in response to Fukushima. Any signiﬁcant nuclear
renaissance or massive build-out would alter our characterization,
as would any massive phase-out. Lastly, we limit our assessment
to nuclear generated electricity and its fuel cycle, and thus exclude
risks posed by nuclear explosives and nuclear weapons, except for
those facilities (such as reprocessing spent fuel) that are dual use.
3. Results and discussion
We quantify four identiﬁable dimensions of risk: (i) historical
frequency of accidents, (ii) historical costs, (iii) the presence of socalled “dragon kings” and extreme events, and (iv) expected future
costs.
In terms of frequency, panel (I) of Fig. 1 plots the number of
events with at least $20 million in damage (and standard errors) per
reactor per year, calculated on 5 year windows spanning 1960 to
2014. The main message here is that the rate of events has dropped
substantially since the 1960s, and may have stabilized since the late
1980s. In panel (II) of Fig. 1 the rate of events is calculated running
away from the Chernobyl accident in both directions. From here it
is clear there was a signiﬁcant decline in event frequency after the
Chernobyl accident, and the rate of events since that drop has been
roughly stable, indicating that Chernobyl was a catalyst for change
that decreased the rate of events, but not necessarily the size of
each event. Rate estimates for 2014 remain in a conservative range
of 0.0025–0.0035, or 1–1.4 events per year over the entire nuclear
ﬂeet. The methodology used here is described in SM2.

3
Sellaﬁeld in the United Kingdom, for instance, is home to commercial reactors,
research reactors, waste repositories, and reprocessing facilities and Fukushima
Daichi in Japan was home to commercial reactors and waste repositories.
4
The analysis here is focused on events with at least $20 million USD in damage.
These events are more visible and thus the dataset is more likely to be complete
above this threshold. Therefore statistics on this subset will be more reliable than
when considering smaller events. Further, these large events are most relevant as
they drive the total risk level. For instance, the ten most costly events contribute
approximately 94% of total costs to date.

Fig. 1. Frequency, damage, and severity of nuclear power accidents.
Panel (I) plots the rate (annual number of events with cost in excess of USD 20 million per reactor) calculated for ﬁve year periods, with standard error bars given.
Panel (II) plots the rate estimate running both backward and forward from the Chernobyl accident in 1987, bounded by standard errors.
Panel (III) plots the NAMS (Nuclear Accident Magnitude Scale) and damage/cost data according to their CCDF (Complementary Cumulative Distribution Function). The CCDF
of the cost data is given for periods both before and after the accident at Three Mile Island (TMI) in 1979. The dashed line overlaid on the NAMS CCDF is an Exponential ﬁt
for the 15 largest points. The dashed line overlaid on the post TMI cost CCDF is a Pareto ﬁt for the 90 largest points. The x marks indicate events that are outlying.
Panel (IV) plots the logarithm of damage/cost versus the INES (International Nuclear Event Scale) scores for each event. The median and quartiles of damage are given for
each INES level with enough points. A linear regression ﬁt to the scatterplot is overlaid.

In terms of historical severity, panel (III) of Fig. 1 plots both
cost and the Nuclear Accident Magnitude Scale (NAMS) [9] according to a complementary cumulative distribution function (CCDF)
described in SM3. As the ﬁgure demonstrates, the damage CCDFs
corresponding to the periods of before and after the Three Mile
Island (TMI) major accident of 1979 are different. It is most plausible that this change was a reaction to TMI, which involved both
improving safety standards as well as reporting more events.
We also ﬁnd that the heavy tailed Pareto distributions are insufﬁcient to account for the extreme empirical tails in the sense
that a few exceptional events are “outliers”, or better said, are
dragon-kings, revealing the existence of transient ampliﬁcation
mechanisms. Such dragon-kings are found to “coexist with power
laws in the distributions of event sizes under a broad range of conditions in a large variety of systems” [23]. As described in SM4, the
presence of dragon-kings provides a diagnostic for the existence of
causal factors behind accidents not apparent from the main Pareto
model used for the distribution. The dragon-kings are shown with
X marks in panel (III) of Fig. 1. The main point here is that postTMI moderate severity events are suppressed but extreme events
escalate to the extent that statistically signiﬁcant dragon-kings
emerge in both NAMS and damage, exhibiting a runaway disaster
regime.

Next, bringing together models for rates and magnitudes, we
quantify the current risk level for the existing nuclear ﬂeet, which
may be used as a status-quo characterization of the future risk
level using the methods described in SM5. Presuming a low rate
= 0.002, and without considering the effect of dragon-kings, the
0.99 quantile is $54.3 billion, almost ﬁve times the estimated damage from Three Mile Island. Presuming the moderate rate = 0.003,
with the dragon-king effect, this quantile is $331.6 billion, which is
almost double the estimated damage of Fukushima. In other words,
there is a 1% probability each year that an accident occurs that leads
to a loss of at least $331.6 billion. Such large numbers do not appear
to be taken into account in standard calculations on the economics
of nuclear power [24]. Moreover, according to our analysis, with
388 reactors in operation, there is a 50% probability of a Fukushimalike event (or more costly) every 60–150 years, and a Three Mile
Island event (or more costly) every 10–20 years.
Finally, panel (IV) of Fig. 1 compares our estimated costs with
INES scores, indicating inconsistencies where events deviate from
the exponential growth in cost qualiﬁed by the line in the logarithmic scale. The multitude of dots above or below the INES scale
strongly suggest it fails to adequately capture the magnitude of
events. For instance, Fukushima (the largest event) would need
to have an INES score of 10.6 to be consistent. Further, there is

considerable uncertainty in the INES scores as evidenced by the
overlapping costs.
4. Six conclusions and policy implications
Our study reveals six important conclusions about the risks
of nuclear power. First, concerning event frequency, our analysis
shows that the rate of civil nuclear accidents over time since 1952
decreased signiﬁcantly from the 1970s, reaching what appears to
be a stable level of around 0.003 events per plant per year. In
this sense, nuclear power is getting safer, although this improvement could be offset by the construction and operation of many
new facilities. We ﬁnd concrete evidence of a history of learning
from previous accidents within the industry, especially the significant reduction in event frequency after the Chernobyl accident
in 1986, and a suppression of moderately large cost events after
TMI.
Second, however, is that these past reforms, rather than minimizing risk, have apparently spawned the prevalence of dragon
kings and accidents with major costs. Chernobyl and Fukushima
are both such dragon kings, as they together represent 84 percent
of the total damage in our dataset. The morphology of nuclear accident risk has altered from more frequent, less costly events to less
frequent, more costly events.
Third, existing databases are woefully incomplete when it
comes to the reporting of nuclear incidents and accidents. For
instance, only half of the events in our database have INES scores,
and thousands upon thousands of small events – but with the
potential to cascade into larger ones – remain unreported. As the
authors of [14] concluded, “many nuclear safety related events
occur year after year, all over the world, in all types of nuclear plants
and in all reactor designs and that there are very serious events that
go either entirely unnoticed by the broader public or remain signiﬁcantly under-evaluated when it comes to their potential risk.”
In Ukraine, for example, most nuclear energy accidents and
incidents have not been included in databases over the past
several years, although state Media confirmed their occurrence.
A fully transparent, centralized source of reliable data on nuclear
accidents is needed; one that enables planners, investors, and even
nuclear regulators to better comprehend, and then weigh, nuclear
risks. Such full disclosure will need to be balanced with the legitimate security concerns of the nuclear industry and the need to
avoid promoting a culture of panic and hysteria.
Fourth, apart from being incomplete, industry standard tools
such as the INES scale of the IAEA are inadequate and inconsistent at identifying and projecting nuclear accident risk, especially
related to dragon kings. For the costs to be consistent with the
INES scores, the Fukushima disaster would need to be between an
INES level of 10 and 11, rather than the maximum level of 7. To
use an analogy, the INES scale is like the antiquated Mercalli scale
for earthquake magnitudes, which was replaced by the continuous physically-based Richter scale. Instead of INES, we
recommend the use of continuous scales genuinely based on
relevant physical variables (radiation emission as in NAMS)
and/or economic metrics (dollar costs as proposed here) and
that these scales be publicly disclosed for as many events as
possible, including all of those in our database.
Fifth, we need to better understand “near misses,” “false
negatives,” “minor mishaps,” and “residual risk” [14]. Our study has
focused only on “extreme risk,” that is, accidents that precipitated
at least 20 million in damages, but an entire class of narrow
escapes exist, unplanned or unanticipated events and warnings

5

http://ec.europa.eu/environment/seveso/.

99

that never resulted in damage [25,26]. In the European Union, for
example, legislation called the Seveso directive5 has
emphasized, since 1982, the importance of near-misses for
hazardous accidents on land, especially in the oil and gas
industry. A similar directive ought to be considered for the
nuclear industry, and it requires a complete data set of both small
and large events to properly quantify the frequency with which
small events escalate into larger ones.
Sixth, future frequency and severity of accidents are perhaps
unacceptably high. While the nuclear industry can be characterized by an impressive improvement in incident prevention and
safety procedures, our thorough analysis of this new data shows
that, when a nuclear event of at least $20 million in damage occurs,
the probability that it transforms into a catastrophe with damage
larger than one billion dollars is almost ten percent. Under the
status quo, we project at least one Fukushima-scale dragon king
(or larger) accident with 50% probability every 60–150 years. The
analysis of data submitted by the states that provide the INES as
well as of their official Media reports about the events and
equipment condition at nuclear power plants shows that another
major accident will most probably occur at a nuclear power plant
in Ukraine. For example, there is an 80% probability that a Three
Mile Island event (or more costly) can occur at Ukraine’s Rivne or
South-Ukraine nuclear power plants over the next 5 years. And,
more common but still expensive events of about $20 million will
occur with a frequency of about one per year–making accidents a
relatively routine part of nuclear power’s future.
In conclusion, although the frequency of events per reactor has
become less common, the relative frequency with which
events cascade into “dragon king” extremes is large enough that,
when multiplied by severity, the aggregate risk to society is still
very high. To effectively reduce this risk, the possibility of
Chernobyl and Fukushima sized events needs to be better
anticipated and then more effectively managed.
Acknowledgments
To solicit as much critical feedback as possible, we posted a
working paper using a different methodology and data set on this
topic in April, 2015 available here http://arxiv.org/abs/1504.02380.
The working paper does not replicate the data presented in this
study, although it does host publicly our data set so that readers
and others can continually improve the robustness and
completeness of its contents. We also thank seven anonymous
reviewers for extremely helpful comments on earlier versions of
this draft, as well as colleagues MV Ramana from Princeton
University, Per Peterson from the University of California Berkeley,
Mycle Schenider from the World Nuclear Industry Status Report,
Mark Cooper and Peter Bradford from Vermont Law School, and
Andy Stirling and Gordon MacKerron from the University of
Sussex. Despite their input, the ﬁndings and conclusions in this
study derive only from the authors.
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in
the online version, at http://dx.doi.org/10.1016/j.erss.2015.12.026.
References
[1] Reuters Special Report: Help wanted in Fukushima, October25, (2013),
available at http://www.reuters.com/article/2013/10/25/us-fukushimaworkers-specialreport-idUSBRE99O04320131025.
[2] John E. Ten Hoeve, Mark Z. Jacobson, Worldwide health effects of the
Fukushima Daiichi nuclear accident, Energy Environ. Sci. 5 (2012) 8758.
[3] Lei Huang, Ying Zhou, Yuting Han, James K. Hammitt, Jun Bi, Yang Liu, Effect
of the Fukushima nuclear accident on the risk perception of residents near a
nuclear power plant in China, PNAS 110 (49) (2013) 19742–19747